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The total graph and regular graph of a commutative ring
Abstract Let R be a commutative ring. The total graph of R , denoted by T ( Γ ( R ) ) is a graph with all elements of R as vertices, and two distinct vertices x , y ∈ R , are adjacent if and only ifExpand
Divisors on graphs, binomial and monomial ideals, and cellular resolutions
We study various binomial and monomial ideals arising in the theory of divisors, orientations, and matroids on graphs. We use ideas from potential theory on graphs and from the theory of DelaunayExpand
Cellular resolutions from mapping cones
This work describes a regular CW-complex that supports the resolutions of Herzog and Takayama in the case that I has a 'regular decomposition function', and recovers other known cellular resolutions, including the 'box of complexes' resolutions of Corso, Nagel, and Reiner and the related 'homomorphism complex' resolutionsof Dochtermann and Engstrom. Expand
Monomial ideals and toric rings of Hibi type arising from a finite poset
In this paper we study monomial ideals attached to posets, introduce generalized Hibi rings and investigate their algebraic and homological properties. The main tools to study these objects areExpand
Prime splittings of determinantal ideals
ABSTRACT We consider determinantal ideals, where the generating minors are encoded in a hypergraph. We study when the generating minors form a Gröbner basis. In this case, the ideal is radical, andExpand
Shellable Cactus Graphs
In this paper a new class of vertex decomposable graphs are determined. Moreover, all shellable and sequentially Cohen-Macaulay cactus graphs (i.e., connected graphs in which each edge belongs to atExpand
A Novel Implementation of G-Fuzzy Logic Controller Algorithm on Mobile Robot Motion Planning Problem
A genetic algorithm is used to find the optimal path for a mobile robot to move in a dynamic environment expressed by a map with nodes and links using GA and fuzzy Algorithms. Expand
Divisors on graphs, orientations, syzygies, and system reliability
We study various ideals arising in the theory of system reliability. We use ideas from the theory of divisors, orientations, and matroids on graphs to describe the minimal polyhedral cellularExpand
Divisors on Graphs, Connected Flags, and Syzygies
We study the binomial and monomial ideals arising from linear equivalence of divisors on graphs from the point of view of Grobner theory. We give an explicit description of a minimal Grobner basisExpand
Generalized Permutohedra from Probabilistic Graphical Models
This work gives a construction of this polytope, up to equivalence of normal fans, as a Minkowski sum of matroid polytopes and applies this geometric insight to construct a new ordering-based search algorithm for causal inference via directed acyclic graphical models. Expand